Question

now present age of father and son is in the ratio 8 is to 5 then there after 4 years the ratio is 3 is to 2 then the present ages of the father and son​

Answer 1

Given :-

ratio between the present ages of father and his son is 8 : 5

let their present ages be 8x and 5x respectively.

ATQ,

after 4 years, their ages will be in the ratio 3 : 2

➡ (8x + 4)/(5x + 4) = 3/2

by cross multiplication, we get

➡ 2(8x + 4) = 3(5x + 4)

➡ 16x + 8 = 15x + 12

➡ 16x - 15x = 12 - 8

➡ x = 4

hence the present ages are :-

• of father = 8x = 32 yrs

• of son = 5x = 20 yrs

VERIFICATION :-

LHS :-

= (32 + 4)/(20 + 4)

= 36/24

= 3/2

RHS :-

= 3/2

LHS = RHS, hence verified!

btw how did the father become father at the age of only 12?? :/

Answer 2

• Let present age of farher be 8M and present age of son be 5M.

》 After 4 years, the ratio of father and son age become 3:2.

Now..

Age of father = (8M + 4) years

Age of son = (5M + 4) years

According to question,

=> $\dfrac{8M\:+\:4}{5M\:+\:4}$ = $\dfrac{3}{2}$

Cross multiply them

=> 2(8M + 4) = 3(5M + 4)

=> 16M + 8 = 15M + 12

=> 16M - 15M = 12 - 8

=> M = 4

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Present age of father = 8(4) = 32 years.

Present age of son = 5(4) = 20 years.

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☆ VERIFICATION:

From above calculations we have M = 4

Put value of M in this: $\dfrac{8M\:+\:4}{5M\:+\:4}$ = $\dfrac{3}{2}$

=> $\dfrac{8(4)\:+\:4}{5(4)\:+\:4}$ = $\dfrac{3}{2}$

=> $\dfrac{32\:+\:4}{20\:+\:4}$ = $\dfrac{3}{2}$

=> $\dfrac{36}{24}$ = $\dfrac{3}{2}$

=> $\dfrac{3}{2}$ = $\dfrac{3}{2}$

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